/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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MAYBE
We consider the system theBenchmark.

We are asked to determine termination of the following first-order TRS.

  0 : [] --> o 
  U101 : [o * o * o] --> o 
  U102 : [o * o * o] --> o 
  U103 : [o * o * o] --> o 
  U104 : [o * o * o] --> o 
  U105 : [o * o] --> o 
  U106 : [o] --> o 
  U11 : [o * o] --> o 
  U111 : [o * o * o] --> o 
  U112 : [o * o * o] --> o 
  U113 : [o * o * o] --> o 
  U114 : [o * o] --> o 
  U12 : [o * o] --> o 
  U121 : [o * o] --> o 
  U122 : [o] --> o 
  U13 : [o] --> o 
  U131 : [o * o * o * o] --> o 
  U132 : [o * o * o * o] --> o 
  U133 : [o * o * o * o] --> o 
  U134 : [o * o * o * o] --> o 
  U135 : [o * o * o * o] --> o 
  U136 : [o * o * o * o] --> o 
  U21 : [o * o] --> o 
  U22 : [o * o] --> o 
  U23 : [o] --> o 
  U31 : [o * o] --> o 
  U32 : [o * o] --> o 
  U33 : [o] --> o 
  U41 : [o * o * o] --> o 
  U42 : [o * o * o] --> o 
  U43 : [o * o * o] --> o 
  U44 : [o * o * o] --> o 
  U45 : [o * o] --> o 
  U46 : [o] --> o 
  U51 : [o * o] --> o 
  U52 : [o] --> o 
  U61 : [o * o] --> o 
  U62 : [o] --> o 
  U71 : [o] --> o 
  U81 : [o] --> o 
  U91 : [o * o * o] --> o 
  U92 : [o * o * o] --> o 
  U93 : [o * o * o] --> o 
  U94 : [o * o * o] --> o 
  U95 : [o * o] --> o 
  U96 : [o] --> o 
  active : [o] --> o 
  cons : [o * o] --> o 
  isNat : [o] --> o 
  isNatIList : [o] --> o 
  isNatIListKind : [o] --> o 
  isNatKind : [o] --> o 
  isNatList : [o] --> o 
  length : [o] --> o 
  mark : [o] --> o 
  nil : [] --> o 
  s : [o] --> o 
  take : [o * o] --> o 
  tt : [] --> o 
  zeros : [] --> o 

  active(zeros) => mark(cons(0, zeros)) 
  active(U101(tt, X, Y)) => mark(U102(isNatKind(X), X, Y)) 
  active(U102(tt, X, Y)) => mark(U103(isNatIListKind(Y), X, Y)) 
  active(U103(tt, X, Y)) => mark(U104(isNatIListKind(Y), X, Y)) 
  active(U104(tt, X, Y)) => mark(U105(isNat(X), Y)) 
  active(U105(tt, X)) => mark(U106(isNatIList(X))) 
  active(U106(tt)) => mark(tt) 
  active(U11(tt, X)) => mark(U12(isNatIListKind(X), X)) 
  active(U111(tt, X, Y)) => mark(U112(isNatIListKind(X), X, Y)) 
  active(U112(tt, X, Y)) => mark(U113(isNat(Y), X, Y)) 
  active(U113(tt, X, Y)) => mark(U114(isNatKind(Y), X)) 
  active(U114(tt, X)) => mark(s(length(X))) 
  active(U12(tt, X)) => mark(U13(isNatList(X))) 
  active(U121(tt, X)) => mark(U122(isNatIListKind(X))) 
  active(U122(tt)) => mark(nil) 
  active(U13(tt)) => mark(tt) 
  active(U131(tt, X, Y, Z)) => mark(U132(isNatIListKind(X), X, Y, Z)) 
  active(U132(tt, X, Y, Z)) => mark(U133(isNat(Y), X, Y, Z)) 
  active(U133(tt, X, Y, Z)) => mark(U134(isNatKind(Y), X, Y, Z)) 
  active(U134(tt, X, Y, Z)) => mark(U135(isNat(Z), X, Y, Z)) 
  active(U135(tt, X, Y, Z)) => mark(U136(isNatKind(Z), X, Y, Z)) 
  active(U136(tt, X, Y, Z)) => mark(cons(Z, take(Y, X))) 
  active(U21(tt, X)) => mark(U22(isNatKind(X), X)) 
  active(U22(tt, X)) => mark(U23(isNat(X))) 
  active(U23(tt)) => mark(tt) 
  active(U31(tt, X)) => mark(U32(isNatIListKind(X), X)) 
  active(U32(tt, X)) => mark(U33(isNatList(X))) 
  active(U33(tt)) => mark(tt) 
  active(U41(tt, X, Y)) => mark(U42(isNatKind(X), X, Y)) 
  active(U42(tt, X, Y)) => mark(U43(isNatIListKind(Y), X, Y)) 
  active(U43(tt, X, Y)) => mark(U44(isNatIListKind(Y), X, Y)) 
  active(U44(tt, X, Y)) => mark(U45(isNat(X), Y)) 
  active(U45(tt, X)) => mark(U46(isNatIList(X))) 
  active(U46(tt)) => mark(tt) 
  active(U51(tt, X)) => mark(U52(isNatIListKind(X))) 
  active(U52(tt)) => mark(tt) 
  active(U61(tt, X)) => mark(U62(isNatIListKind(X))) 
  active(U62(tt)) => mark(tt) 
  active(U71(tt)) => mark(tt) 
  active(U81(tt)) => mark(tt) 
  active(U91(tt, X, Y)) => mark(U92(isNatKind(X), X, Y)) 
  active(U92(tt, X, Y)) => mark(U93(isNatIListKind(Y), X, Y)) 
  active(U93(tt, X, Y)) => mark(U94(isNatIListKind(Y), X, Y)) 
  active(U94(tt, X, Y)) => mark(U95(isNat(X), Y)) 
  active(U95(tt, X)) => mark(U96(isNatList(X))) 
  active(U96(tt)) => mark(tt) 
  active(isNat(0)) => mark(tt) 
  active(isNat(length(X))) => mark(U11(isNatIListKind(X), X)) 
  active(isNat(s(X))) => mark(U21(isNatKind(X), X)) 
  active(isNatIList(X)) => mark(U31(isNatIListKind(X), X)) 
  active(isNatIList(zeros)) => mark(tt) 
  active(isNatIList(cons(X, Y))) => mark(U41(isNatKind(X), X, Y)) 
  active(isNatIListKind(nil)) => mark(tt) 
  active(isNatIListKind(zeros)) => mark(tt) 
  active(isNatIListKind(cons(X, Y))) => mark(U51(isNatKind(X), Y)) 
  active(isNatIListKind(take(X, Y))) => mark(U61(isNatKind(X), Y)) 
  active(isNatKind(0)) => mark(tt) 
  active(isNatKind(length(X))) => mark(U71(isNatIListKind(X))) 
  active(isNatKind(s(X))) => mark(U81(isNatKind(X))) 
  active(isNatList(nil)) => mark(tt) 
  active(isNatList(cons(X, Y))) => mark(U91(isNatKind(X), X, Y)) 
  active(isNatList(take(X, Y))) => mark(U101(isNatKind(X), X, Y)) 
  active(length(nil)) => mark(0) 
  active(length(cons(X, Y))) => mark(U111(isNatList(Y), Y, X)) 
  active(take(0, X)) => mark(U121(isNatIList(X), X)) 
  active(take(s(X), cons(Y, Z))) => mark(U131(isNatIList(Z), Z, X, Y)) 
  mark(zeros) => active(zeros) 
  mark(cons(X, Y)) => active(cons(mark(X), Y)) 
  mark(0) => active(0) 
  mark(U101(X, Y, Z)) => active(U101(mark(X), Y, Z)) 
  mark(tt) => active(tt) 
  mark(U102(X, Y, Z)) => active(U102(mark(X), Y, Z)) 
  mark(isNatKind(X)) => active(isNatKind(X)) 
  mark(U103(X, Y, Z)) => active(U103(mark(X), Y, Z)) 
  mark(isNatIListKind(X)) => active(isNatIListKind(X)) 
  mark(U104(X, Y, Z)) => active(U104(mark(X), Y, Z)) 
  mark(U105(X, Y)) => active(U105(mark(X), Y)) 
  mark(isNat(X)) => active(isNat(X)) 
  mark(U106(X)) => active(U106(mark(X))) 
  mark(isNatIList(X)) => active(isNatIList(X)) 
  mark(U11(X, Y)) => active(U11(mark(X), Y)) 
  mark(U12(X, Y)) => active(U12(mark(X), Y)) 
  mark(U111(X, Y, Z)) => active(U111(mark(X), Y, Z)) 
  mark(U112(X, Y, Z)) => active(U112(mark(X), Y, Z)) 
  mark(U113(X, Y, Z)) => active(U113(mark(X), Y, Z)) 
  mark(U114(X, Y)) => active(U114(mark(X), Y)) 
  mark(s(X)) => active(s(mark(X))) 
  mark(length(X)) => active(length(mark(X))) 
  mark(U13(X)) => active(U13(mark(X))) 
  mark(isNatList(X)) => active(isNatList(X)) 
  mark(U121(X, Y)) => active(U121(mark(X), Y)) 
  mark(U122(X)) => active(U122(mark(X))) 
  mark(nil) => active(nil) 
  mark(U131(X, Y, Z, U)) => active(U131(mark(X), Y, Z, U)) 
  mark(U132(X, Y, Z, U)) => active(U132(mark(X), Y, Z, U)) 
  mark(U133(X, Y, Z, U)) => active(U133(mark(X), Y, Z, U)) 
  mark(U134(X, Y, Z, U)) => active(U134(mark(X), Y, Z, U)) 
  mark(U135(X, Y, Z, U)) => active(U135(mark(X), Y, Z, U)) 
  mark(U136(X, Y, Z, U)) => active(U136(mark(X), Y, Z, U)) 
  mark(take(X, Y)) => active(take(mark(X), mark(Y))) 
  mark(U21(X, Y)) => active(U21(mark(X), Y)) 
  mark(U22(X, Y)) => active(U22(mark(X), Y)) 
  mark(U23(X)) => active(U23(mark(X))) 
  mark(U31(X, Y)) => active(U31(mark(X), Y)) 
  mark(U32(X, Y)) => active(U32(mark(X), Y)) 
  mark(U33(X)) => active(U33(mark(X))) 
  mark(U41(X, Y, Z)) => active(U41(mark(X), Y, Z)) 
  mark(U42(X, Y, Z)) => active(U42(mark(X), Y, Z)) 
  mark(U43(X, Y, Z)) => active(U43(mark(X), Y, Z)) 
  mark(U44(X, Y, Z)) => active(U44(mark(X), Y, Z)) 
  mark(U45(X, Y)) => active(U45(mark(X), Y)) 
  mark(U46(X)) => active(U46(mark(X))) 
  mark(U51(X, Y)) => active(U51(mark(X), Y)) 
  mark(U52(X)) => active(U52(mark(X))) 
  mark(U61(X, Y)) => active(U61(mark(X), Y)) 
  mark(U62(X)) => active(U62(mark(X))) 
  mark(U71(X)) => active(U71(mark(X))) 
  mark(U81(X)) => active(U81(mark(X))) 
  mark(U91(X, Y, Z)) => active(U91(mark(X), Y, Z)) 
  mark(U92(X, Y, Z)) => active(U92(mark(X), Y, Z)) 
  mark(U93(X, Y, Z)) => active(U93(mark(X), Y, Z)) 
  mark(U94(X, Y, Z)) => active(U94(mark(X), Y, Z)) 
  mark(U95(X, Y)) => active(U95(mark(X), Y)) 
  mark(U96(X)) => active(U96(mark(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) 
  U101(mark(X), Y, Z) => U101(X, Y, Z) 
  U101(X, mark(Y), Z) => U101(X, Y, Z) 
  U101(X, Y, mark(Z)) => U101(X, Y, Z) 
  U101(active(X), Y, Z) => U101(X, Y, Z) 
  U101(X, active(Y), Z) => U101(X, Y, Z) 
  U101(X, Y, active(Z)) => U101(X, Y, Z) 
  U102(mark(X), Y, Z) => U102(X, Y, Z) 
  U102(X, mark(Y), Z) => U102(X, Y, Z) 
  U102(X, Y, mark(Z)) => U102(X, Y, Z) 
  U102(active(X), Y, Z) => U102(X, Y, Z) 
  U102(X, active(Y), Z) => U102(X, Y, Z) 
  U102(X, Y, active(Z)) => U102(X, Y, Z) 
  isNatKind(mark(X)) => isNatKind(X) 
  isNatKind(active(X)) => isNatKind(X) 
  U103(mark(X), Y, Z) => U103(X, Y, Z) 
  U103(X, mark(Y), Z) => U103(X, Y, Z) 
  U103(X, Y, mark(Z)) => U103(X, Y, Z) 
  U103(active(X), Y, Z) => U103(X, Y, Z) 
  U103(X, active(Y), Z) => U103(X, Y, Z) 
  U103(X, Y, active(Z)) => U103(X, Y, Z) 
  isNatIListKind(mark(X)) => isNatIListKind(X) 
  isNatIListKind(active(X)) => isNatIListKind(X) 
  U104(mark(X), Y, Z) => U104(X, Y, Z) 
  U104(X, mark(Y), Z) => U104(X, Y, Z) 
  U104(X, Y, mark(Z)) => U104(X, Y, Z) 
  U104(active(X), Y, Z) => U104(X, Y, Z) 
  U104(X, active(Y), Z) => U104(X, Y, Z) 
  U104(X, Y, active(Z)) => U104(X, Y, Z) 
  U105(mark(X), Y) => U105(X, Y) 
  U105(X, mark(Y)) => U105(X, Y) 
  U105(active(X), Y) => U105(X, Y) 
  U105(X, active(Y)) => U105(X, Y) 
  isNat(mark(X)) => isNat(X) 
  isNat(active(X)) => isNat(X) 
  U106(mark(X)) => U106(X) 
  U106(active(X)) => U106(X) 
  isNatIList(mark(X)) => isNatIList(X) 
  isNatIList(active(X)) => isNatIList(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) 
  U12(mark(X), Y) => U12(X, Y) 
  U12(X, mark(Y)) => U12(X, Y) 
  U12(active(X), Y) => U12(X, Y) 
  U12(X, active(Y)) => U12(X, Y) 
  U111(mark(X), Y, Z) => U111(X, Y, Z) 
  U111(X, mark(Y), Z) => U111(X, Y, Z) 
  U111(X, Y, mark(Z)) => U111(X, Y, Z) 
  U111(active(X), Y, Z) => U111(X, Y, Z) 
  U111(X, active(Y), Z) => U111(X, Y, Z) 
  U111(X, Y, active(Z)) => U111(X, Y, Z) 
  U112(mark(X), Y, Z) => U112(X, Y, Z) 
  U112(X, mark(Y), Z) => U112(X, Y, Z) 
  U112(X, Y, mark(Z)) => U112(X, Y, Z) 
  U112(active(X), Y, Z) => U112(X, Y, Z) 
  U112(X, active(Y), Z) => U112(X, Y, Z) 
  U112(X, Y, active(Z)) => U112(X, Y, Z) 
  U113(mark(X), Y, Z) => U113(X, Y, Z) 
  U113(X, mark(Y), Z) => U113(X, Y, Z) 
  U113(X, Y, mark(Z)) => U113(X, Y, Z) 
  U113(active(X), Y, Z) => U113(X, Y, Z) 
  U113(X, active(Y), Z) => U113(X, Y, Z) 
  U113(X, Y, active(Z)) => U113(X, Y, Z) 
  U114(mark(X), Y) => U114(X, Y) 
  U114(X, mark(Y)) => U114(X, Y) 
  U114(active(X), Y) => U114(X, Y) 
  U114(X, active(Y)) => U114(X, Y) 
  s(mark(X)) => s(X) 
  s(active(X)) => s(X) 
  length(mark(X)) => length(X) 
  length(active(X)) => length(X) 
  U13(mark(X)) => U13(X) 
  U13(active(X)) => U13(X) 
  isNatList(mark(X)) => isNatList(X) 
  isNatList(active(X)) => isNatList(X) 
  U121(mark(X), Y) => U121(X, Y) 
  U121(X, mark(Y)) => U121(X, Y) 
  U121(active(X), Y) => U121(X, Y) 
  U121(X, active(Y)) => U121(X, Y) 
  U122(mark(X)) => U122(X) 
  U122(active(X)) => U122(X) 
  U131(mark(X), Y, Z, U) => U131(X, Y, Z, U) 
  U131(X, mark(Y), Z, U) => U131(X, Y, Z, U) 
  U131(X, Y, mark(Z), U) => U131(X, Y, Z, U) 
  U131(X, Y, Z, mark(U)) => U131(X, Y, Z, U) 
  U131(active(X), Y, Z, U) => U131(X, Y, Z, U) 
  U131(X, active(Y), Z, U) => U131(X, Y, Z, U) 
  U131(X, Y, active(Z), U) => U131(X, Y, Z, U) 
  U131(X, Y, Z, active(U)) => U131(X, Y, Z, U) 
  U132(mark(X), Y, Z, U) => U132(X, Y, Z, U) 
  U132(X, mark(Y), Z, U) => U132(X, Y, Z, U) 
  U132(X, Y, mark(Z), U) => U132(X, Y, Z, U) 
  U132(X, Y, Z, mark(U)) => U132(X, Y, Z, U) 
  U132(active(X), Y, Z, U) => U132(X, Y, Z, U) 
  U132(X, active(Y), Z, U) => U132(X, Y, Z, U) 
  U132(X, Y, active(Z), U) => U132(X, Y, Z, U) 
  U132(X, Y, Z, active(U)) => U132(X, Y, Z, U) 
  U133(mark(X), Y, Z, U) => U133(X, Y, Z, U) 
  U133(X, mark(Y), Z, U) => U133(X, Y, Z, U) 
  U133(X, Y, mark(Z), U) => U133(X, Y, Z, U) 
  U133(X, Y, Z, mark(U)) => U133(X, Y, Z, U) 
  U133(active(X), Y, Z, U) => U133(X, Y, Z, U) 
  U133(X, active(Y), Z, U) => U133(X, Y, Z, U) 
  U133(X, Y, active(Z), U) => U133(X, Y, Z, U) 
  U133(X, Y, Z, active(U)) => U133(X, Y, Z, U) 
  U134(mark(X), Y, Z, U) => U134(X, Y, Z, U) 
  U134(X, mark(Y), Z, U) => U134(X, Y, Z, U) 
  U134(X, Y, mark(Z), U) => U134(X, Y, Z, U) 
  U134(X, Y, Z, mark(U)) => U134(X, Y, Z, U) 
  U134(active(X), Y, Z, U) => U134(X, Y, Z, U) 
  U134(X, active(Y), Z, U) => U134(X, Y, Z, U) 
  U134(X, Y, active(Z), U) => U134(X, Y, Z, U) 
  U134(X, Y, Z, active(U)) => U134(X, Y, Z, U) 
  U135(mark(X), Y, Z, U) => U135(X, Y, Z, U) 
  U135(X, mark(Y), Z, U) => U135(X, Y, Z, U) 
  U135(X, Y, mark(Z), U) => U135(X, Y, Z, U) 
  U135(X, Y, Z, mark(U)) => U135(X, Y, Z, U) 
  U135(active(X), Y, Z, U) => U135(X, Y, Z, U) 
  U135(X, active(Y), Z, U) => U135(X, Y, Z, U) 
  U135(X, Y, active(Z), U) => U135(X, Y, Z, U) 
  U135(X, Y, Z, active(U)) => U135(X, Y, Z, U) 
  U136(mark(X), Y, Z, U) => U136(X, Y, Z, U) 
  U136(X, mark(Y), Z, U) => U136(X, Y, Z, U) 
  U136(X, Y, mark(Z), U) => U136(X, Y, Z, U) 
  U136(X, Y, Z, mark(U)) => U136(X, Y, Z, U) 
  U136(active(X), Y, Z, U) => U136(X, Y, Z, U) 
  U136(X, active(Y), Z, U) => U136(X, Y, Z, U) 
  U136(X, Y, active(Z), U) => U136(X, Y, Z, U) 
  U136(X, Y, Z, active(U)) => U136(X, Y, Z, U) 
  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) 
  U21(mark(X), Y) => U21(X, Y) 
  U21(X, mark(Y)) => U21(X, Y) 
  U21(active(X), Y) => U21(X, Y) 
  U21(X, active(Y)) => U21(X, Y) 
  U22(mark(X), Y) => U22(X, Y) 
  U22(X, mark(Y)) => U22(X, Y) 
  U22(active(X), Y) => U22(X, Y) 
  U22(X, active(Y)) => U22(X, Y) 
  U23(mark(X)) => U23(X) 
  U23(active(X)) => U23(X) 
  U31(mark(X), Y) => U31(X, Y) 
  U31(X, mark(Y)) => U31(X, Y) 
  U31(active(X), Y) => U31(X, Y) 
  U31(X, active(Y)) => U31(X, Y) 
  U32(mark(X), Y) => U32(X, Y) 
  U32(X, mark(Y)) => U32(X, Y) 
  U32(active(X), Y) => U32(X, Y) 
  U32(X, active(Y)) => U32(X, Y) 
  U33(mark(X)) => U33(X) 
  U33(active(X)) => U33(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) 
  U42(mark(X), Y, Z) => U42(X, Y, Z) 
  U42(X, mark(Y), Z) => U42(X, Y, Z) 
  U42(X, Y, mark(Z)) => U42(X, Y, Z) 
  U42(active(X), Y, Z) => U42(X, Y, Z) 
  U42(X, active(Y), Z) => U42(X, Y, Z) 
  U42(X, Y, active(Z)) => U42(X, Y, Z) 
  U43(mark(X), Y, Z) => U43(X, Y, Z) 
  U43(X, mark(Y), Z) => U43(X, Y, Z) 
  U43(X, Y, mark(Z)) => U43(X, Y, Z) 
  U43(active(X), Y, Z) => U43(X, Y, Z) 
  U43(X, active(Y), Z) => U43(X, Y, Z) 
  U43(X, Y, active(Z)) => U43(X, Y, Z) 
  U44(mark(X), Y, Z) => U44(X, Y, Z) 
  U44(X, mark(Y), Z) => U44(X, Y, Z) 
  U44(X, Y, mark(Z)) => U44(X, Y, Z) 
  U44(active(X), Y, Z) => U44(X, Y, Z) 
  U44(X, active(Y), Z) => U44(X, Y, Z) 
  U44(X, Y, active(Z)) => U44(X, Y, Z) 
  U45(mark(X), Y) => U45(X, Y) 
  U45(X, mark(Y)) => U45(X, Y) 
  U45(active(X), Y) => U45(X, Y) 
  U45(X, active(Y)) => U45(X, Y) 
  U46(mark(X)) => U46(X) 
  U46(active(X)) => U46(X) 
  U51(mark(X), Y) => U51(X, Y) 
  U51(X, mark(Y)) => U51(X, Y) 
  U51(active(X), Y) => U51(X, Y) 
  U51(X, active(Y)) => U51(X, Y) 
  U52(mark(X)) => U52(X) 
  U52(active(X)) => U52(X) 
  U61(mark(X), Y) => U61(X, Y) 
  U61(X, mark(Y)) => U61(X, Y) 
  U61(active(X), Y) => U61(X, Y) 
  U61(X, active(Y)) => U61(X, Y) 
  U62(mark(X)) => U62(X) 
  U62(active(X)) => U62(X) 
  U71(mark(X)) => U71(X) 
  U71(active(X)) => U71(X) 
  U81(mark(X)) => U81(X) 
  U81(active(X)) => U81(X) 
  U91(mark(X), Y, Z) => U91(X, Y, Z) 
  U91(X, mark(Y), Z) => U91(X, Y, Z) 
  U91(X, Y, mark(Z)) => U91(X, Y, Z) 
  U91(active(X), Y, Z) => U91(X, Y, Z) 
  U91(X, active(Y), Z) => U91(X, Y, Z) 
  U91(X, Y, active(Z)) => U91(X, Y, Z) 
  U92(mark(X), Y, Z) => U92(X, Y, Z) 
  U92(X, mark(Y), Z) => U92(X, Y, Z) 
  U92(X, Y, mark(Z)) => U92(X, Y, Z) 
  U92(active(X), Y, Z) => U92(X, Y, Z) 
  U92(X, active(Y), Z) => U92(X, Y, Z) 
  U92(X, Y, active(Z)) => U92(X, Y, Z) 
  U93(mark(X), Y, Z) => U93(X, Y, Z) 
  U93(X, mark(Y), Z) => U93(X, Y, Z) 
  U93(X, Y, mark(Z)) => U93(X, Y, Z) 
  U93(active(X), Y, Z) => U93(X, Y, Z) 
  U93(X, active(Y), Z) => U93(X, Y, Z) 
  U93(X, Y, active(Z)) => U93(X, Y, Z) 
  U94(mark(X), Y, Z) => U94(X, Y, Z) 
  U94(X, mark(Y), Z) => U94(X, Y, Z) 
  U94(X, Y, mark(Z)) => U94(X, Y, Z) 
  U94(active(X), Y, Z) => U94(X, Y, Z) 
  U94(X, active(Y), Z) => U94(X, Y, Z) 
  U94(X, Y, active(Z)) => U94(X, Y, Z) 
  U95(mark(X), Y) => U95(X, Y) 
  U95(X, mark(Y)) => U95(X, Y) 
  U95(active(X), Y) => U95(X, Y) 
  U95(X, active(Y)) => U95(X, Y) 
  U96(mark(X)) => U96(X) 
  U96(active(X)) => U96(X)